Graphing Quadratics in Vertex & Standard Form Worksheets | Made By ... - Free Printable

Let’s solve a few sample problems from the worksheets shown, step by step. We’ll pick one from Vertex Form and one from Standard Form to show you how it works.

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Problem 1 (Vertex Form): Find the vertex of y = 2(x - 4)² + 6

In vertex form:
y = a(x - h)² + k
The vertex is at point (h, k)

Here, the equation is:
y = 2(x - 4)² + 6

So, h = 4, k = 6
→ Vertex is (4, 6)

✔ Check: The number inside the parentheses with x is subtracted, so if it says (x - 4), then h = 4. If it were (x + 3), that would be (x - (-3)), so h = -3. But here it’s minus 4 → h = 4. And the last number is +6 → k = 6.

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Problem 2 (Standard Form): For y = x² - 4x + 3, find the axis of symmetry and vertex

Standard form: y = ax² + bx + c
Here, a = 1, b = -4, c = 3

Axis of Symmetry formula:
x = -b/(2a)

Plug in:
x = -(-4)/(2×1) = 4/2 = 2
→ Axis of Symmetry: x = 2

Now find the vertex. The x-coordinate is 2 (from above). Plug x = 2 into the equation to get y:

y = (2)² - 4(2) + 3
= 4 - 8 + 3
= -1

→ Vertex is (2, -1)

✔ Double-check:
At x = 2, y = 4 - 8 + 3 = -1 ✔️
Formula for AOS used correctly ✔️

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Problem 3 (Graph Matching): Match graph to equation — let’s take y = (x + 2)²

This is vertex form: y = (x - h)² + k → here, h = -2, k = 0 → vertex at (-2, 0)

Also, since a = 1 (positive), parabola opens up.

Look for a graph with vertex at (-2, 0) and opening upward.

If you see four graphs labeled A–D, and one has its lowest point at x = -2, y = 0, that’s the match.

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Final Answer:
For y = 2(x - 4)² + 6 → Vertex: (4, 6)
For y = x² - 4x + 3 → Axis of Symmetry: x = 2, Vertex: (2, -1)
For y = (x + 2)² → Vertex at (-2, 0), opens up — match to graph with those features.